1. Pitch and Interval
1. Octaves and the Major-Minor Tonal System
2. Half Steps and Whole Steps
3. Interval
4, Ear ‘Training
2. Keys and Scales
1. Major Keys and Scales
2. Minor Keys and Scales
3. The Circle of Fifths
3. Triads and Chords
1. Triads
. Naming ‘Triads
. Beginning Harmonic Analysis
. Cadence in Music
. Consonance and Dissonance
. Beyond Triads: Naming Other Chords
AUB WN
Octaves and the Major-Minor Tonal System
Introduces the relationship between frequency, octaves, major, minor, and
chromatic scales, and tonal music.
Where Octaves Come From
Musical notes, like all sounds, are made of sound waves. The sound waves
that make musical notes are very evenly-spaced waves, and the qualities of
these regular waves - for example how big they are or how far apart they
are - affect the sound of the note. A note can be high or low, depending on
how often (how frequently) one of its waves arrives at your ear. When
scientists and engineers talk about how high or low a sound is, they talk
about its frequency. The higher the frequency of a note, the higher it
sounds. They can measure the frequency of notes, and like most
measurements, these will be numbers, like "440 vibrations per second."
High and Low Frequencies
SCAVAVAVAVAVAVAVAY
VAD DAL
lacae
A sound that has a shorter
wavelength has a higher
frequency and a higher pitch.
But people have been making music and talking about music since long
before we knew that sounds were waves with frequencies. So when
musicians talk about how high or low a note sounds, they usually don't talk
about frequency; they talk about the note's pitch. And instead of numbers,
they give the notes names, like "C". (For example, musicians call the note
with frequency "440 vibrations per second" an "A".)
But to see where octaves come from, let's talk about frequencies a little
more. Imagine a few men are singing a song together. Nobody is singing
harmony; they are all singing the same pitch - the same frequency - for each
note.
Now some women join in the song. They can't sing where the men are
singing; that's too low for their voices. Instead they sing notes that are
exactly double the frequency that the men are singing. That means their
note has exactly two waves for each one wave that the men's note has.
These two frequencies fit so well together that it sounds like the women are
singing the same notes as the men, in the same key. They are just singing
them one octave higher. Any note that is twice the frequency of another
note is one octave higher.
Notes that are one octave apart are so closely related to each other that
musicians give them the same name. A note that is an octave higher or
lower than a note named "C natural" will also be named "C natural". A note
that is one (or more) octaves higher or lower than an "F sharp" will also be
an "F sharp". (For more discussion of how notes are related because of their
frequencies, see The Harmonic Series, Standing Waves and Musical
Instruments, and Standing Waves and Wind Instruments. )
Octave Frequencies
When two notes are
one octave apart, one
has a frequency
exactly two times
higher than the other -
it has twice as many
waves. These waves
fit together so well, in
the instrument, and in
the air, and in your
ears, that they sound
almost like different
versions of the same
note.
Naming Octaves
The notes in different octaves are so closely related that when musicians
talk about a note, a "G" for example, it often doesn't matter which G they
are talking about. We can talk about the "F sharp" in a G major scale
without mentioning which octave the scale or the F sharp are in, because
the scale is the same in every octave. Because of this, many discussions of
music theory don't bother naming octaves. Informally, musicians often
speak of "the B on the staff" or the "A above the staff", if it's clear which
staff they're talking about.
But there are also two formal systems for naming the notes in a particular
octave. Many musicians use Helmholtz notation. Others prefer scientific
pitch notation, which simply labels the octaves with numbers, starting with
C1 for the lowest C on a full-sized keyboard. Figure 3 shows the names of
the octaves most commonly used in music.
Naming Octaves
4
Say: "Contra" "Great" "Small" "One-line" "Two-line" "Three-line"
Helmholtz: CC C c re cu cm
Scientific: C, Cc, Cc, C, Cc, C,
The octaves are named from one C to the next higher
C. For example, all the notes in between "one line c"
and "two line c" are "one line" notes.
The octave below contra can be labelled CCC or Co; higher octaves can be
labelled with higher numbers or more lines. Octaves are named from one C
to the next higher C. For example, all the notes between "great C" and
"small C" are "great". One-line c is also often called "middle C". No
other notes are called "middle", only the C.
Example:
Naming Notes within a Particular Octave
Each note is considered to be in the same octave as
the C below it.
Exercise:
Problem: Give the correct octave name for each note.
_—_——— —————
Fe
Solution:
= ———
al dil ° . b! g gil dili
SS ee ee
q G ea E e' a al
Dividing the Octave into Scales
The word "octave" comes from a Latin root meaning "eight". It seems an
odd name for a frequency that is two times, not eight times, higher. The
octave was named by musicians who were more interested in how octaves
are divided into scales, than in how their frequencies are related. Octaves
aren't the only notes that sound good together. The people in different
musical traditions have different ideas about what notes they think sound
best together. In the Western musical tradition - which includes most
familiar music from Europe and the Americas - the octave is divided up into
twelve equally spaced notes. If you play all twelve of these notes within one
octave you are playing a chromatic scale. Other musical traditions -
traditional Chinese music for example - have divided the octave differently
and so they use different scales. (Please see Major Keys and Scales, Minor
Keys and Scales, and Scales that aren’t Major or Minor for more about
this.)
You may be thinking "OK, that's twelve notes; that still has nothing to do
with the number eight", but out of those twelve notes, only seven are used
in any particular major or minor scale. Add the first note of the next octave,
so that you have that a "complete"-sounding scale ("do-re-mi-fa-so-la-ti"
and then "do" again), and you have the eight notes of the octave. These are
the diatonic scales, and they are the basis of most Western music.
Now take a look at the piano keyboard. Only seven letter names are used to
name notes: A, B, C, D, E, F, and G. The eighth note would, of course, be
the next A, beginning the next octave. To name the other notes, the notes on
the black piano keys, you have to use a sharp or flat sign.
Keyboard
The white keys are the
natural notes. Black
keys can only be
named using sharps or
flats. The pattern
repeats at the eighth
tone of a scale, the
octave.
Whether it is a popular song, a classical symphony, or an old folk tune,
most of the music that feels comfortable and familiar (to Western listeners)
is based on either a major or minor scale. It is tonal music that mostly uses
only seven of the notes within an octave: only one of the possible A's (A
sharp, A natural, or A flat), one of the possible B's (B sharp, B natural, or B
flat), and so on. The other notes in the chromatic scale are (usually) used
sparingly to add interest or to (temporarily) change the key in the middle of
the music. For more on the keys and scales that are the basis of tonal music,
see Major Keys and Scales and Minor Keys and Scales.
Half Steps and Whole Steps
The pitch of a note is how high or low it sounds. The distance between two
pitches can be measured in half steps and whole steps.
The pitch of a note is how high or low it sounds. Musicians often find it
useful to talk about how much higher or lower one note is than another.
This distance between two pitches is called the interval between them. In
Western music, the small interval from one note to the next closest note
higher or lower is called a half step or semi-tone.
Half Steps
Three half-step intervals: between C and C sharp (or D flat); between
E and F; and between G sharp (or A flat) and A.
G?
nN
m
n_
Listen to the half steps in [link].
The intervals in [link] look different on a staff; sometimes they are on the
same line, sometimes not. But it is clear at the keyboard that in each case
there is no note in between them.
So a scale that goes up or down by half steps, a chromatic scale, plays all
the notes on both the white and black keys of a piano. It also plays all the
notes easily available on most Western instruments. (A few instruments,
like trombone and violin, can easily play pitches that aren't in the chromatic
scale, but even they usually don't.)
One Octave Chromatic Scale
All intervals in a chromatic scale are
half steps. The result is a scale that
plays all the notes easily available on
most instruments.
Listen to a chromatic scale.
If you go up or down two half steps from one note to another, then those
notes are a whole step, or whole tone apart.
Whole Steps
Three whole step intervals: between C and D; between E and F sharp;
and between G sharp and A sharp (or A flat and B flat).
Fe G* AF
A whole tone scale, a scale made only of whole steps, sounds very different
from a chromatic scale.
Whole Tone Scale
bop pee
All intervals in a whole tone
scale are whole steps.
Listen to a whole tone scale.
You can count any number of whole steps or half steps between notes; just
remember to count all sharp or flat notes (the black keys on a keyboard) as
well as all the natural notes (the white keys) that are in between.
Example:
The interval between C and the F above it is 5 half steps, or two and a half
Going from C up to F takes
five half steps.
Exercise:
Problem:
Identify the intervals below in terms of half steps and whole steps. If
you have trouble keeping track of the notes, use a piano keyboard, a
written chromatic scale, or the chromatic fingerings for your
instrument to count half steps.
3 half steps 4 half steps 8 half steps 7 half steps
(15 steps) (2 whole steps) (4 whole steps) (35 steps)
5 half steps 6 half steps 7 half steps 9 half steps
(2 : steps) (3 whole steps) (35 whole steps) (45 steps)
Exercise:
Problem:
Fill in the second note of the interval indicated in each measure. If you
need staff paper for this exercise, you can print out this staff paper
PDF file.
O—————————————
Shalfstepshigher 1wholesteplower 2wholestepslower 9 half steps lower
——————— =
1 whole step higher _—_1 half step lower 2 whole steps higher ‘11 half steps lower
ES Sf
Ol? ee er : ee
3 whole steps higher 3halfstepslower 1 half step higher 7 half steps lower
Solution:
Shalfstepshigher 1wholesteplower 2wholestepslower 9 half steps lower
lwhole stephigher 1halfsteplower 2wholestepshigher 11 half steps lower
3 whole steps higher 3halfstepslower 1 half step higher 7 half steps lower
If your answer is different, check to see if you have
written a different enharmonic spelling of the note in
the answer. For example, the B flat could be written as
an A sharp.
Interval
The distance between two pitches is the interval between them. The name of an interval
depends both on how the notes are written and the actual distance between the notes as
measured in half steps.
The Distance Between Pitches
The interval between two notes is the distance between the two pitches - in other words,
how much higher or lower one note is than the other. This concept is so important that it is
dissonance without referring to intervals. So if you want to learn music theory, it would be a
good idea to spend some time getting comfortable with the concepts below and practicing
identifying intervals.
Scientists usually describe the distance between two pitches in terms of the difference
between their frequencies. Musicians find it more useful to talk about interval. Intervals can
be described using half steps and whole steps. For example, you can say "B natural is a half
step below C natural", or "E flat is a step and a half above C natural". But when we talk
about larger intervals in the major/minor system, there is a more convenient and descriptive
way to name them.
Naming Intervals
The first step in naming the interval is to find the distance between the notes as they are
written on the staff. Count every line and every space in between the notes, as well as the
lines or spaces that the notes are on. This gives you the number for the interval.
Example:
Counting Intervals
Count 1 2 3 4 5 6
To find the interval, count the lines or spaces that the two notes are on as well as all the
lines or spaces in between. The interval between B and D is a third. The interval between A
and F is a sixth. Note that, at this stage, key signature, clef, and accidentals do not matter at
all.
The simple intervals are one octave or smaller.
Simple Intervals
Prime Second Third Fourth Fifth Sixth Seventh Octave
If you like you can listen to each interval as written in [link]: prime, second, third, fourth,
[missing resource: fifth.mid]sixth, seventh, [missing resource: octave.mid]
Compound intervals are larger than an octave.
Compound Intervals
: 2 2
e
Ninth Tenth Eleventh Twelfth,and so on...
Listen to the compound intervals in [link]: ninth, tenth, eleventh.
Exercise:
Problem: Name the intervals.
J
Third Fifth Octave Second Seventh Fourth
Exercise:
Problem: Write a note that will give the named interval.
Second Octave Fifth Third Sixth Fourth
Lower Lower Higher Higher Higher Lower
Second Octave Fifth Third Sixth Fourth
Lower Lower Higher Higher Higher Lower
Classifying Intervals
So far, the actual distance, in half-steps, between the two notes has not mattered. But a third
made up of three half-steps sounds different from a third made up of four half-steps. And a
fifth made up of seven half-steps sounds very different from one of only six half-steps. So in
the second step of identifying an interval, clef, key_signature, and accidentals become
important.
——————
Three Half Steps = A Third Four Half Steps = A different Third
Seven Half Steps = A Fifth Six Half Steps = A different Fifth
A to C natural and A to C sharp are both thirds, but A
to C sharp is a larger interval, with a different sound.
The difference between the intervals A to E natural
and A to E flat is even more noticeable.
Listen to the differences in the thirds and the fifths in [link].
So the second step to naming an interval is to classify it based on the number of half steps in
the interval. Familiarity with the chromatic scale is necessary to do this accurately.
Perfect Intervals
Primes, octaves, fourths, and fifths can be perfect intervals.
Note: These intervals are never classified as major or minor, although they can be
augmented or diminished (see below).
What makes these particular intervals perfect? The physics of sound waves (acoustics)
shows us that the notes of a perfect interval are very closely related to each other. (For more
information on this, see Frequency, Wavelength, and Pitch and Harmonic Series.) Because
they are so closely related, they sound particularly good together, a fact that has been
noticed since at least the times of classical Greece, and probably even longer. (Both the
octave and the perfect fifth have prominent positions in most of the world's musical
traditions.) Because they sound so closely related to each other, they have been given the
name "perfect" intervals.
Note: Actually, modern equal temperament tuning does not give the harmonic-series-based
pure perfect fourths and fifths. For the music-theory purpose of identifying intervals, this
does not matter. To learn more about how tuning affects intervals as they are actually
played, see Tuning Systems.
A perfect prime is also called a unison. It is two notes that are the same pitch. A perfect
octave is the "same" note an octave - 12 half-steps - higher or lower. A perfect 5th is 7 half-
steps. A perfect fourth is 5 half-steps.
Example:
Perfect Intervals
‘ 2 2 2 2 2
Unison Octave Perfect Fourth Perfect Fifth
Listen to the octave, perfect fourth, and perfect fifth.
Major and Minor Intervals
Seconds, thirds, sixths, and sevenths can be major intervals or minor intervals. The minor
interval is always a half-step smaller than the major interval.
Major and Minor Intervals
e 1 half-step = minor second (m2)
e 2 half-steps = major second (M2)
e 3 half-steps = minor third (m3)
e 4half-steps = major third (M3)
e 8 half-steps = minor sixth (m6)
e 9 half-steps = major sixth (M6)
e 10 half-steps = minor seventh (m7)
e 11 half-steps = major seventh (M7)
Example:
Major and Minor Intervals
Minor Second Major Second Minor Third Major Third
cy) e o °e e
Minor Sixth Major Sixth Minor Seventh Major Seventh
minor seventh, and major seventh.
Exercise:
Problem: Give the complete name for each interval.
Solution:
- Oo
Major Second Minor Third Perfect Fifth Perfect Fourth
Perfect Octave Minor Sixth Unison Major Seventh
(Perfect prime)
Major Sixth Minor Seventh Major Third Minor Second
Exercise:
Problem: Fill in the second note of the interval given.
O——————————
e
PS higher P4 lower m2 lower Pprime
a
2 =
M3 higher m7 lower P 8ve higher M6 higher
m6 lower M2 higher PS lower m3 higher
PS higher P4 lower m2 lower Pprime
M3 higher m7 lower P 8ve higher M6 higher
Augmented and Diminished Intervals
If an interval is a half-step larger than a perfect or a major interval, it is called augmented.
An interval that is a half-step smaller than a perfect or a minor interval is called diminished.
A double sharp or double flat is sometimes needed to write an augmented or diminished
interval correctly. Always remember, though, that it is the actual distance in half steps
between the notes that determines the type of interval, not whether the notes are written as
natural, sharp, or double-sharp.
Example:
Some Diminished and Augmented Intervals
Augmented Prime Diminished Second Augmented Third Diminished Sixth
Augmented Seventh Diminished Octave Augmented Fourth Diminished Fifth
surprised that the augmented fourth and diminished fifth sound the same?
Exercise:
Problem: Write a note that will give the named interval.
Augmented Octave Diminished Sixth Augmented Fourth Diminished Second
Higher Lower Higher Lower
Augmented Prime Diminished Seventh Augmented Third Diminished Fifth
Higher Lower Higher Lower
Solution:
Augmented Octave Diminished Sixth Augmented Fourth Diminished Second
Higher Lower Higher Lower
Augmented Prime Diminished Seventh Augmented Third Diminished Fifth
Higher Lower Higher Lower
As mentioned above, the diminished fifth and augmented fourth sound the same. Both are
six half-steps, or three whole tones, so another term for this interval is a tritone. In Western
Music, this unique interval, which cannot be spelled as a major, minor, or perfect interval, is
considered unusually dissonant and unstable (tending to want to resolve to another interval).
You have probably noticed by now that the tritone is not the only interval that can be
"spelled" in more than one way. In fact, because of enharmonic spellings, the interval for
any two pitches can be written in various ways. A major third could be written as a
diminished fourth, for example, or a minor second as an augmented prime. Always classify
the interval as it is written; the composer had a reason for writing it that way. That
reason sometimes has to do with subtle differences in the way different written notes will be
interpreted by performers, but it is mostly a matter of placing the notes correctly in the
context of the key, the chord, and the evolving harmony, (Please see Beginning Harmonic
Analysis for more on that subject.)
Enharmonic Intervals
MajorThird soundsthe sameas Diminished Fourth
e e
MinorSecond soundsthesameas Augmented Prime
Any interval can be written in a
variety of ways using enharmonic
spelling. Always classify the
interval as it is written.
Inverting Intervals
To invert any interval, simply imagine that one of the notes has moved one octave, so that
the higher note has become the lower and vice-versa. Because inverting an interval only
involves moving one note by an octave (it is still essentially the "same" note in the tonal
system), intervals that are inversions of each other have a very close relationship in the
tonal system.
Inverting Intervals
From F From B
e 2
Down to C: Up to C: Down to D: Up to D:
Perfect Fourth Perfect Fifth Major Sixth Minor Third
To find the inversion of an interval
1. To name the new interval, subtract the name of the old interval from 9.
2. The inversion of a perfect interval is still perfect.
3. The inversion of a major interval is minor, and of a minor interval is major.
4. The inversion of an augmented interval is diminished and of a diminished interval is
augmented.
Example:
Minor Seventh Inversion is a Major Second
9-7=2
Minor inverts to major
e) eo 2
Exercise:
Problem: What are the inversions of the following intervals?
1. Augmented third
2. Perfect fifth
3. Diminished fifth
4. Major seventh
5. Minor sixth
Solution:
1. Diminished sixth
2. Perfect fourth
3. Augmented fourth
4. Minor second
5. Major third
Summary
Here is a quick summary of the above information, for reference.
Number Common Example, Alternate Example,
of half ; ?
Spelling from C Spelling from C
steps
Perfect ee
0 Unison C Diminished D double
(P1) Second flat
Inversion
Octave
(P8)
10
11
Minor
Second
(m2)
Major
Second
(M2)
Minor
Third
(m3)
Major
Third
(M3)
Perfect
Fourth
(P4)
Tritone
(TT)
Perfect
Fifth (P5)
Minor
Sixth
(m6)
Major
Sixth
(M6)
Minor
Seventh
(m7)
Major
Seventh
(M7)
D flat
E flat
F sharp
or G flat
-)
A flat
B flat
Augmented
Unison
Diminished
Third
Augmented
Second
Diminished
Fourth
Augmented
Third
Augmented
Fourth or
Diminished
Fifth
Diminished
Sixth
Augmented
Fifth
Diminished
Seventh
Augmented
Sixth
Diminished
Octave
C sharp
E double
flat
D sharp
F flat
E sharp
F sharp
or G flat
A double
flat
G sharp
B double
flat
A sharp
C' flat
Major
Seventh
(M7)
Minor
Seventh
(m7)
Major
Sixth
(M6)
Minor
Sixth
(m6)
Perfect
Fifth (P5)
Tritone
(TT)
Perfect
Fourth
(P4)
Major
Third
(M3)
Minor
Third
(m3)
Major
Second
(M2)
Minor
Second
(m2)
12 Perfect C' Augmented B sharp Perfect
Octave Seventh Unison
(P8) (P1)
The examples given name the note reached if one starts on C, and goes up the named
interval.
Summary Notes: Perfect Intervals
e A perfect prime is often called a unison. It is two notes of the same pitch.
e A perfect octave is often simply called an octave. It is the next "note with the same
name".
e Perfect intervals - unison, fourth, fifth, and octave - are never called major or minor
Summary Notes: Augmented and Diminished Intervals
e An augmented interval is one half step larger than the perfect or major interval.
e A diminished interval is one half step smaller than the perfect or minor interval.
Summary Notes: Inversions of Intervals
To find the inversion's number name, subtract the interval number name from 9.
e Inversions of perfect intervals are perfect.
e Inversions of major intervals are minor, and inversions of minor intervals are major.
e Inversions of augmented intervals are diminished, and inversions of diminished
intervals are augmented.
Ear Training
Ear training develops the basic listening skills of the music student. Here
are some suggestions for developing the various ear training skills,
including a downloadable game to play.
What is Ear Training?
When musicians talk about ear, they don't mean the sense organ itself so
much as the brain's ability to perceive, distinguish, and understand what the
ear has heard. The term ear training refers to teaching musicians to
recognize information about notes and chords just by hearing them.
A few people have what is called perfect pitch or absolute pitch. These
people, when they hear music, can tell you exactly what they are hearing:
the G above middle C, for example, or the first inversion of an F minor
chord. A few musicians with particularly perceptive ears can even tell you
that a piano is tuned a few cents higher than the one that they play at home.
This is an unusual skill that even most trained musicians do not have, and
research seems to suggest that if you don't have it at a very early age, you
cannot develop it. (For more on this subject, you may want to look up
Robert Jourdain's Music, the Brain, and Ecstasy: How Music Captures our
Imagination.)
However, most musicians can be trained to recognize relative pitch. In
other words, if you play two notes, they can tell you that one of them is a
major third higher than the other. If you play four chords in a row, they can
tell you that you played a tonic-subdominant-dominant seventh-tonic (I-IV-
V7-I) chord progression.
Fortunately, having relative pitch is good enough, and for many musicians
may even be more useful than perfect pitch, because of the way Western
music is conceived. Since all major keys are so similar, a piece in a major
key will sound almost exactly the same whether you play it in C major or D
major. The thing that matters is not what note you start on, but how all the
notes are related to each other and to the "home" note (the tonic) of the key.
If someone really wants the piece to be in a different key (because it's easier
to sing or play in that key, or just because they want it to sound higher or
lower), the whole thing can be transposed, but the only difference that
would make (in the sound) is that the entire piece will sound higher or
lower. Most listeners would not even notice the difference, unless you
played it in both keys, one right after the other.
Note:All minor keys are also heard by most listeners as interchangeable,
but there are important differences between major keys and minor keys. In
fact, the differences in sound between a major key and a minor key is one
of the first differences that a musician should be able to hear. If you would
like to see whether your "ear" can recognize the difference between major
So, you often don't need to know exactly what notes or chords are being
played. Simply having an ear well-trained in "relative pitch" is extremely
useful in many ways. Guitar and piano players can figure out chord
progressions just by listening to them, and then play the progressions in
their favorite keys. Other instrumentalists can play a favorite tune without a
written copy of it, just by knowing what the interval to the next note must
be. Composers and music arrangers can jot down a piece of music without
having to "pick it out" on an instrument to find the notes and chords they
want. And of course, ear training is crucial to any musician who wants to
play jazz or any type of improvisation. Given a well-trained "ear", any
musical idea that you "hear" in your head, you can play. And ear training is
also crucial for those interested in music theory, musicology, or just being
able to write down a tune accurately.
As with all other musical skills, there are many different levels and kinds of
proficiency. One musician may be very good at "playing by ear", but may
not even read music and cannot name intervals or write the music down.
Another may be very good at "taking dictation" (writing down the music
they hear), and yet feel unable to do jazz improvisation. As always, the key
is to practice the particular skills that you want to develop.
Ear Training Skills
Tuning
This is the most basic ear training skill, crucial to being able to play music
that people will want to hear.
Suggestions
e At the beginner level, work with a skilled musician who can teach you
how to tune your instrument and help you identify and fix tuning
problems.
e Play with other musicians often. (Playing along with recordings does
not teach good tuning skills.) Don't just tune at the beginning of
rehearsals and performances. Listen at all times and be ready to retune
any note whenever necessary.
e Spend as much time as necessary tuning whenever you play. Do not
(knowingly) practice while out of tune; if you do, it will slow down
your ear training tremendously. Whenever possible, until you are good
at tuning, get someone else to help you tune every time you play.
e Practice tuning quickly and accurately. Learn any alternate fingerings
and other "tricks" available on your instrument for fine-tuning each
note as you play.
Playing Chords By Ear
For instruments that play chordal accompaniments, this is an incredibly
useful skill.
Suggestions
e You do not have to learn to read music to be able to do this, but it is
very helpful to know a little bit about music theory so that you can
predict which chords are most likely to happen in a song. Try starting
with Beginning Harmonic Analysis.
e Really listen to the chord progressions to the songs you do know. What
do they sound like? Play the same progressions in different keys and
listen to how that does and also does not change the sound of the
progression. Change the bass notes of the chords to see how that
changes the sound of the progression to your ears. Change fingerings
and chord voicings, and again listen carefully to how that changes the
sound to your ears.
e Practice figuring out the chords to familiar songs (that you don't know
the chords to). For songs that you do know the chords to, try playing
them in an unfamiliar key, or see if you can change or add chords to
make a new harmony that still fits the melody.
e A teacher who understands harmony can help tremendously with this
particular skill. Even if you don't normally take lessons, you might
want to consider having a series of lessons on this. Find a teacher who
is willing and able to teach you specifically about harmony and typical
chord progressions.
Playing Tunes by Ear
This is fun to be able to do, makes it easy to increase your repertoire, and is
an important step in being able to improvise.
Suggestions
e Just do it! The best way to learn this skill is to spend some of your
practice time trying to play tunes you know and like.
e Once you start getting good at this, see how quickly you can get a new
tune down. How few mistakes can you make the first time you try it?
Can you "recover" quickly from a mistake by making it sound like a
bit of improvisation?
e If you play a melody instrument (one that plays only one note at a
time), there are different bits of information that help you recognize
what the next note will be: how far it is from the note you are on (see
Interval), where it is in the key (see Beginning Harmonic Analysis) or
where it is in the chord (see Triads). These three things are all related
to each other, of course - and a musician with a well-trained ear will be
aware of all of them, at least subconsciously - but you may find at first
that one works better for you than the others. You may want to
experiment: is it easier for you to think of the next note as being a
perfect fourth higher than the note you are on, or as being the root of
the chord, or as being the fifth note in the scale of the key?
e As of this writing, petersax-online had many exercises graded from
simple to more difficult to help the beginner practice playing what you
hear.
Improvisation
This is the skill you need for jazz. Blues, rock, and many Non-Western
traditions also use improvisation.
Suggestions
e Know your scales and arpeggios. A good improviser, given the name
of a chord, can quickly play not only the notes of the chord but also the
scale implied by the chord. Any decent book on playing jazz, or any
teacher familiar with jazz, will introduce the student to these chords
and scales.
e There are now many book/CD combinations available to help the
beginning improviser in many different genres and on many different
instruments. A good book of this type will give the student a chance to
improvise on many familiar tunes, and some also introduce the music
theory involved. At the time of this writing, one source of a large
variety of such books was jazzbooks.com .
e The exercises at the petersax site mentioned above would also be
useful for the beginning improviser.
e Listen to jazz often. Listen to the improvisers you admire, and if a
particular solo really appeals to you, listen to it many times, find the
notes on your instrument, and then try writing it down as accurately as
you can. Many famous improvisors, when interviewed, mention how
useful it was to them to learn from other soloists by transcribing their
solos in this way.
e Figure out how to play your favorite jazz (or blues or rock) licks (short
motives that show up in many pieces in the same genre) on your
instrument. Practice stringing them together in ways that make sense to
you, but are different from what you've heard. Add your own
variations.
e Find a teacher who is familiar with the type of improvisation you want
to learn, join a jazz band, and/or get together with other musicians who
also want to practise improvisation and take turns playing
background/rhythm for each other.
Recognizing Intervals and Writing Music Down
This is the skill that allowed Beethoven to continue composing
masterpieces even after he became deaf. If you are interested in composing,
arranging, music theory, musicology, or just being able to write down a tune
quickly and accurately, you'll want to be able to make that quick connection
between what you hear and written music.
Suggestions
¢ Before you can do this, you must know your major and minor keys and
scales and your Intervals. You may also want to understand
Transposition, since you may find it easier to work in some keys than
in others.
e As of this writing, Teoria Musical was a free ear training website that
worked well, and the commercial site TrainEar included a free online
version.
e Once again, practice is the best way to become good at this. Start with
tunes that you know well, but don't know what the (written) notes are.
Listen to them in your head (or play a recording) while trying to write
them down. Then play what you have written, noticing where you
were correct and where you made mistakes. Which intervals are you
good at hearing? Which do you have trouble identifying? Do you often
mistake one particular interval for another? Do you tend to identify a
note by its interval from the previous note or by its place in the chord
or in the key? Answering these questions will help you improve more
quickly.
¢ Some people find it easier to learn to recognize intervals if they
associate each interval with a familiar tune. (For example, in the
familiar song from The Sound of Music that begins "Do, a deer, a
female deer...", all the intervals in the phrase "a female deer" are major
thirds, and every interval in the phrase "someday I'll wish upon a star"
in the song "Somewhere Over the Rainbow" is a minor third.) The tune
should be very familiar, so when trying to hear a tritone, some people
will prefer thinking of the beginning of "The Simpsons" theme; others
will prefer the beginning of "Maria" from West Side Story. If you think
this method will work for you, try playing the interval you are having
trouble hearing, and see what tune it reminds you of. As of this
writing, TrainEar included a long list, with links to recordings, or
songs that can be associated with various intervals.
Try searching at YouTube for "Interval song" or "ear training" to find
videos that you might find helpful.
Major Keys and Scales
A scale is a list of all the notes in a key. Major scales all follow the same
interval pattern.
The simple, sing-along, nursery rhymes and folk songs we learn as children;
the "catchy" tunes used in advertising jingles; the cheerful, toe-tapping pop
and rock we dance to; the uplifting sounds of a symphony: most music in a
major key has a bright sound that people often describe as cheerful,
inspiring, exciting, or just plain fun.
How are these moods produced? Music in a particular key tends to use only
some of the many possible notes available; these notes are listed in the scale
associated with that key. In major keys, the notes of the scale are often used
to build "bright"-sounding major chords. They also give a strong feeling of
having a tonal center, a note or chord that feels like "home", or "the resting
place", in that key. The "bright"-sounding major chords and the strong
feeling of tonality are what give major keys their happy, pleasant moods.
This contrasts with the moods usually suggested by music that uses minor
keys, scales, and chords. Although it also has a strong tonal center (the
Western tradition of tonal harmony is based on major and minor keys and
scales), music in a minor key is more likely to sound sad, ominous, or
mysterious. In fact, most musicians, and even many non-musicians, can
distinguish major and minor keys just by listening to the music.
Exercise:
Problem:
Listen to these excerpts. Three are in a major key and two in a minor
key. Can you tell which is which simply by listening?
e
Sie
Solution:
1. Major
2. Major
3. Minor
4. Major
o. Minor
Note:If you must determine whether a piece of music is major or minor,
and cannot tell just by listening, you may have to do some simple harmonic
analysis in order to decide.
Tonal Center
A scale starts with the note that names the key. This note is the tonal center
of that key, the note where music in that key feels "at rest". It is also called
the tonic, and it's the "do" in "do-re-mi". For example, music in the key of
A major almost always ends on an A major chord, the chord built on the
note A. It often also begins on that chord, returns to that chord often, and
features a melody and a bass line that also return to the note A often enough
that listeners will know where the tonal center of the music is, even if they
don't realize that they know it. (For more information about the tonic chord
and its relationship to other chords in a key, please see Beginning Harmonic
Analysis.)
Example:
Listen to these examples. Can you hear that they do not feel "done" until
the final tonic is played?
e Example A
e Example B
Major Scales
To find the rest of the notes in a major key, start at the tonic and go up
following this pattern: whole step, whole step, half step, whole step,
whole step, whole step, half step. This will take you to the tonic one
octave higher than where you began, and includes all the notes in the key in
that octave.
Example:
These major scales all follow the same pattern of whole steps and half
steps. They have different sets of notes because the pattern starts on
different notes.
Three Major Scales
e
ey ee NP Ne a ee
Whole Whole Half Whole Whole Whole Half
Step Step Step Step Step Step Step
SS SS
; Ne os ae ae Re Ne
W Ww H Ww Ww W H
All major scales have the same pattern of half
steps and whole steps, beginning on the note
that names the scale - the tonic.
Listen to the difference between the C major, D major, and B flat major
scales.
Exercise:
Problem:
For each note below, write a major scale, one octave, ascending (going
up), beginning on that note. If you're not sure whether a note should be
written as a flat, sharp, or natural, remember that you won't ever skip a
line or space, or write two notes of the scale on the same line or space.
If you need help keeping track of half steps, use a keyboard, a picture
of a keyboard, a written chromatic scale, or the chromatic scale
fingerings for your instrument. If you need more information about
half steps and whole steps, see Half Steps and Whole Steps.
If you need staff paper for this exercise, you can print out this staff
paper PDF file.
Solution:
Notice that although they look completely different, the scales of F
sharp major and G flat major (numbers 5 and 6) sound exactly the
same when played, on a piano as shown in [link], or on any other
instrument using equal temperament tuning. If this surprises you,
please read more about enharmonic scales.
Enharmonic Scales
BEE BW &
Using this figure of a
keyboard, or the
fingerings from your
Own instrument,
notice that the notes
for the F sharp major
scale and the G flat
major scale in [link],
although spelled
differently, will sound
the same.
In the examples above, the sharps and flats are written next to the notes. In
common notation, the sharps and flats that belong in the key will be
written at the beginning of each staff, in the key signature. For more
practice identifying keys and writing key signatures, please see Key
Signature. For more information about how keys are related to each other,
please see The Circle of Fifths.
Note:Do key signatures make music more complicated than it needs to be?
Is there an easier way? Join the discussion at Opening Measures.
Music in Different Major Keys
What difference does key make? Since the major scales all follow the same
pattern, they all sound very much alike. Here is the tune "Row, Row, Row
Your Boat", written in G major and also in D major.
The same tune looks very different when written in two different major
keys.
In D Major
Listen to this tune in G major and in D major. The music may look quite
different, but the only difference when you listen is that one sounds higher
than the other. So why bother with different keys at all? Before equal
temperament became the standard tuning system, major keys sounded more
different from each other than they do now. Even now, there are subtle
differences between the sound of a piece in one key or another, mostly
because of differences in the timbre of various notes on the instruments or
voices involved. But today the most common reason to choose a particular
key is simply that the music is easiest to sing or play in that key. (Please see
Transposition for more about choosing keys.)
Minor Keys and Scales
The interval pattern for minor scales is different from that of major scales.
Every minor key shares a key signature with its relative major. There are
three common types of minor scales: natural minor, melodic minor, and
harmonic minor. Jazz also commonly uses a "dorian minor".
Music in a Minor Key
Each major key uses a different set of notes (its major scale). In each major
scale, however, the notes are arranged in the same major scale pattern and
build the same types of chords that have the same relationships with each
other. (See Beginning Harmonic Analysis for more on this.) So music that
is in, for example, C major, will not sound significantly different from
music that is in, say, D major. But music that is in D minor will have a
different quality, because the notes in the minor scale follow a different
pattern and so have different relationships with each other. Music in minor
keys has a different sound and emotional feel, and develops differently
harmonically. So you can't, for example, transpose a piece from C major to
D minor (or even to C minor) without changing it a great deal. Music that is
in a minor key is sometimes described as sounding more solemn, sad,
mysterious, or ominous than music that is in a major key. To hear some
simple examples in both major and minor keys, see Major Keys and Scales.
Minor Scales
Minor scales sound different from major scales because they are based on a
different pattern of intervals. Just as it did in major scales, starting the
minor scale pattern on a different note will give you a different key
signature, a different set of sharps or flats. The scale that is created by
playing all the notes in a minor key signature is a natural minor scale. To
create a natural minor scale, start on the tonic note and go up the scale using
the interval pattern: whole step, half step, whole step, whole step, half
step, whole step, whole step.
Natural Minor Scale Intervals
———
Vf NM AS ON UOC CON CN
Whole Half Whole Whole Half Whole Whole
Step Step Step Step Step Step Step
er Nr st UOC UN ON OOM
w H w w H w w
SS ——————
Listen to these minor scales.
Exercise:
Problem:
For each note below, write a natural minor scale, one octave, ascending
(going up) beginning on that note. If you need staff paper, you may
print the stall staff paper an file.
= = &
Solution:
1. Aminor _
a
2.G minor :
e
3.B flat minor
4.E minor
5.F minor
6.F sharp minor
Relative Minor and Major Keys
Each minor key shares a key signature with a major key. A minor key is
called the relative minor of the major key that has the same key signature.
Even though they have the same key signature, a minor key and its relative
major sound very different. They have different tonal centers, and each will
feature melodies, harmonies, and chord progressions built around their
(different) tonal centers. In fact, certain strategic accidentals are very useful
in helping establish a strong tonal center in a minor key. These useful
accidentals are featured in the melodic minor and harmonic minor scales.
Comparing Major and Minor Scale Patterns
Minor Scale Pattern: W H W Ww oH Ww w
—
Major Scale Pattern:
Oia cg eee
W =Whole H = Half
Step Step
The interval patterns for major and natural
minor scales are basically the same pattern
starting at different points.
It is easy to predict where the relative minor of a major key can be found.
Notice that the pattern for minor scales overlaps the pattern for major
scales. In other words, they are the same pattern starting in a different place.
(If the patterns were very different, minor key signatures would not be the
Same as major key signatures.) The pattern for the minor scale starts a half
step plus a whole step lower than the major scale pattern, so a relative
minor is always three half steps lower than its relative major. For
example, C minor has the same key signature as E flat major, since E flat is
a minor third higher than C.
Relative Minor
C major: no flats or sharps
—————
C minor: three flats
e)
E flat major: three flats
The C major and C minor scales start on the
same note, but have different key signatures.
C minor and E flat major start on different
notes, but have the same key signature. C
minor is the relative minor of E flat major.
Exercise:
Problem: What are the relative majors of the minor keys in [link]?
Solution:
1. A minor: C major
2. G minor: B flat major
3. B flat minor: D flat major
4. E minor: G major
5. F minor: A flat major
6. F sharp minor: A major
Harmonic and Melodic Minor Scales
Note:Do key signatures make music more complicated than it needs to be?
Is there an easier way? Join the discussion at Opening Measures.
All of the scales above are natural minor scales. They contain only the
notes in the minor key signature. There are two other kinds of minor scales
that are commonly used, both of which include notes that are not in the key
signature. The harmonic minor scale raises the seventh note of the scale
by one half step, whether you are going up or down the scale.
Harmonies in minor keys often use this raised seventh tone in order to make
the music feel more strongly centered on the tonic. (Please see Beginning
Harmonic Analysis for more about this.) In the melodic minor scale, the
sixth and seventh notes of the scale are each raised by one half step
when going up the scale, but return to the natural minor when going
down the scale. Melodies in minor keys often use this particular pattern of
accidentals, so instrumentalists find it useful to practice melodic minor
scales.
Comparing Types of Minor Scales
A Natural Minor s
SSS
A Harmonic Minor so
A Melodic Minor
Listen to the differences between the natural minor, harmonic minor, and
melodic minor scales.
Exercise:
Problem:
Rewrite each scale from [link] as an ascending harmonic minor scale.
Solution:
1. A harmonic minor
a
2.G harmonic minor : 3
Lz
3.B flat harmonic minor
e ros -e
4.E harmonic minor
5.F harmonic minor
6.F sharp harmonic minor
Exercise:
Problem:
Rewrite each scale from [link] as an ascending and descending
melodic minor scale.
Solution:
1. A melodic minor
a
2.G melodic minor
a, 4 Dy
a a
3.B flat melodic minor
——— Se
e
4.E melodic minor
a ae
P fiak
SS |
Jazz and "Dorian Minor"
Major and minor scales are traditionally the basis for Western Music, but
jazz theory also recognizes other scales, based on the medieval church
modes, which are very useful for improvisation. One of the most useful of
these is the scale based on the dorian mode, which is often called the
dorian minor, since it has a basically minor sound. Like any minor scale,
dorian minor may start on any note, but like dorian mode, it is often
illustrated as natural notes beginning on d.
Dorian Minor
The "dorian minor" can be written
as a scale of natural notes starting
on d. Any scale with this interval
pattern can be called a "dorian
minor scale".
Comparing this scale to the natural minor scale makes it easy to see why the
dorian mode sounds minor; only one note is different.
Comparing Dorian and Natural Minors
e
e
You may find it helpful to notice that the "relative major" of the Dorian
begins one whole step lower. (So, for example, D Dorian has the same key
signature as C major.) In fact, the reason that Dorian is so useful in jazz is
that it is the scale used for improvising while a ii chord is being played (for
example, while a d minor chord is played in the key of C major), a chord
which is very common in jazz. (See Beginning Harmonic Analysis for more
about how chords are classified within a key.) The student who is interested
in modal jazz will eventually become acquainted with all of the modal
scales. Each of these is named for the medieval church mode which has the
same interval pattern, and each can be used with a different chord within the
key. Dorian is included here only to explain the common jazz reference to
the "dorian minor" and to give notice to students that the jazz approach to
scales can be quite different from the traditional classical approach.
Comparison of Dorian and Minor Scales
A Natural Minor
A Harmonic Minor
A Melodic Minor
A Dorian Minor »
You may also find it useful to compare the
dorian with the minor scales from [link].
Notice in particular the relationship of the
altered notes in the harmonic, melodic, and
dorian minors.
The Circle of Fifths
Picturing a circle of fifths can help you identify key signatures, find related
keys, and remember the order of sharps and flats in key signatures.
Related Keys
The circle of fifths is a way to arrange keys to show how closely they are
related to each other.
Circle of Fifths
E > Major Key
e = minor key
The major key for each key signature is shown
as a Capital letter; the minor key as a small letter.
In theory, one could continue around the circle
adding flats or sharps (so that B major is also C
flat major, with seven flats, E major is also F flat
major, with 6 flats and a double flat, and so on),
but in practice such key signatures are very rare.
Keys are not considered closely related to each other if they are near each
other in the chromatic scale (or on a keyboard). What makes two keys
"closely related" is having similar key signatures. So the most closely
related key to C major, for example, is A minor, since they have the same
key signature (no sharps and no flats). This puts them in the same "slice" of
the circle. The next most closely related keys to C major would be G major
(or E minor), with one sharp, and F major (or D minor), with only one flat.
The keys that are most distant from C major, with six sharps or six flats, are
on the opposite side of the circle.
The circle of fifths gets its name from the fact that as you go from one
section of the circle to the next, you are going up or down by an interval of
a perfect fifth. If you go up a perfect fifth (clockwise in the circle), you get
the key that has one more sharp or one less flat; if you go down a perfect
fifth (counterclockwise), you get the key that has one more flat or one less
sharp. Since going down by a perfect fifth is the same as going up by a
perfect fourth, the counterclockwise direction is sometimes referred to as a
"circle of fourths". (Please review inverted intervals if this is confusing.)
Example:
The key of D major has two sharps. Using the circle of fifths, we find that
the most closely related major keys (one in each direction) are G major,
with only one sharp, and A major, with three sharps. The relative minors of
all of these keys (B minor, E minor, and F sharp minor) are also closely
related to D major.
Exercise:
Problem:
What are the keys most closely related to E flat major? To A minor?
Solution:
E flat major (3 flats):
e B flat major (2 flats)
e A flat major (4 flats)
e C minor (3 flats)
¢ G minor (2 flats)
e F minor (4 flats)
A minor (no sharps or flats):
e E minor (1 sharp)
e D minor (1 flat)
e C major (no sharps or flats)
¢ G major (1 sharp)
e F major (1 flat)
Exercise:
Problem: Name the major and minor keys for each key signature.
D major B major B flat major G flat major
B minor G sharp minor G minor E flat minor
Key Signatures
If you do not know the order of the sharps and flats, you can also use the
circle of fifths to find these. The first sharp in a key signature is always F
sharp; the second sharp in a key signature is always (a perfect fifth away) C
sharp; the third is always G sharp, and so on, all the way to B sharp.
The first flat in a key signature is always B flat (the same as the last sharp);
the second is always E flat, and so on, all the way to F flat. Notice that, just
as with the key signatures, you add sharps or subtract flats as you go
clockwise around the circle, and add flats or subtract sharps as you go
counterclockwise.
Adding Sharps and Flats to the Key Signature
Add sharps
in this see C
2nd sharp
6th flat
G
Ist sharp
7th flat
3rd sharp
5th flat
D
4th sharp
4th flat
5th sharp
3rd flat
6th sharp
2nd flat
7th sharp
Ist flat
J
Add flats
in this order
B
Each sharp and flat that is added to a key
signature is also a perfect fifth away
from the last sharp or flat that was added.
Exercise:
Problem:
[link] shows that D major has 2 sharps; [link] shows that they are F
sharp and C sharp. After D major, name the next four sharp keys, and
name the sharp that is added with each key.
Solution:
e A major adds G sharp
e E major adds D sharp
e B major adds A sharp
e F sharp major adds E sharp
+}
J
¥ G major D major A major E major B major F sharp major
Exercise:
Problem:
E minor is the first sharp minor key; the first sharp added in both
major and minor keys is always F sharp. Name the next three sharp
minor keys, and the sharp that is added in each key.
Solution:
e B minor adds C sharp
e F sharp minor adds G sharp
e C sharp minor adds D sharp
e
E minor B minor Fsharp minor C sharp minor
Exercise:
Problem:
After B flat major, name the next four flat keys, and name the flat that
is added with each key.
Solution:
e E flat major adds A flat
e A flat major adds D flat
e D flat major adds G flat
e G flat major adds C flat
F major Bflatmajor Eflatmajor Aflatmajor Dflatmajor Gflat major
Triads
Triads are basic three-note chords built of thirds. They can be in root
position, first inversion, or second inversion.
Harmony, in Western music is based on triads. ‘Triads are simple three-note
chords built of thirds.
Triads in Root Position
Triads in Root Position
Fifth of chord _
== Third of chord 2 intervals
Interval of a fifth <3 fa third
e i oO ofa thir
Root of chord
The chords in [link] are written in root position, which is the most basic
way to write a triad. In root position, the root, which is the note that names
the chord, is the lowest note. The third of the chord is written a third
higher than the root, and the fifth of the chord is written a fifth higher than
the root (which is also a third higher than the third of the chord). So the
simplest way to write a triad is as a stack of thirds, in root position.
Note:The type of interval or chord - major, minor, diminished, etc., is not
important when you are determining the position of the chord. To simplify
things, all notes in the examples and exercises below are natural, but it
would not change their position at all if some notes were sharp or flat. It
would, however, change the name of the triad - see Naming Triads.
Exercise:
Problem:
Write a triad in root position using each root given. If you need some
staff paper for exercises you can print this PDF file.
Build Root Position Triads:
(Example)
Solution:
Build Root Position Triads:
(Example)
First and Second Inversions
Any other chord that has the same-named notes as a root position chord is
considered to be essentially the same chord in a different position. In other
words, all chords that have only D naturals, F sharps, and A naturals, are
considered D major chords.
Note:But if you change the pitch or spelling of any note in the triad, you
have changed the chord (see Naming Triads). For example, if the F sharps
are written as G flats, or if the A's are sharp instead of natural, you have a
different chord, not an inversion of the same chord. If you add notes, you
have also changed the name of the chord (see Beyond Triads). You cannot
call one chord the inversion of another if either one of them has a note
that does not share a name (for example "F sharp" or "B natural")
with a note in the other chord.
If the third of the chord is the lowest note, the chord is in first inversion. If
the fifth of the chord is the lowest note, the chord is in second inversion. A
chord in second inversion may also be called a six-four chord, because the
intervals in it are a sixth and a fourth.
Three C major chords
—————_
Root Position First Inversion Second Inversion
It does not matter how far the higher notes are from the lowest note, or how
many of each note there are (at different octaves or on different
instruments); all that matters is which note is lowest. (In fact, one of the
notes may not even be written, only implied by the context of the chord in a
piece of music. A practiced ear will tell you what the missing note is; we
won't worry about that here.) To decide what position a chord is in, move
the notes to make a stack of thirds and identify the root.
Example:
Notes are G, D,and B. Rewrite as thirds:
2
<=
e Gis still the lowest note,
so the chord was already
in root position.
Example:
Notes are a G,2 C's, and an E.
Rewrite G, C, and E as thirds:
e 2
vo Root position has
C as its lowest note.
Lowest note in original chord
is the fifth in root position,
so it was in second inversion.
Exercise:
Problem:
Rewrite each chord in root position, and name the original position of
the chord.
(Example)
Second Inversion Root Position First Inversion Root Position
First Inversion Second Inversion Second Inversion First Inversion
Naming Triads
The name of a chord depends on the intervals between its notes when the
chord is in root position.
The position that a chord is in does make a difference in how it sounds, but
it is a fairly small difference. Listen to a G major chord in three different
positions.
G major chord in three different
positions.
A much bigger difference in the chord's sound comes from the intervals
between the root-position notes of the chord. For example, if the B in one of
the chords above was changed to a B flat, you would still have a G triad,
but the chord would now sound very different. So chords are named
according to the intervals between the notes when the chord is in root
position. Listen to four different G chords.
These are also all G chords, but they are four
different G chords. The intervals between the
notes are different, so the chords sound very
different.
Major and Minor Chords
The most commonly used triads form major chords and minor chords. All
major chords and minor chords have an interval of a perfect fifth between
the root and the fifth of the chord. A perfect fifth (7 half-steps) can be
divided into a major third (4 half-steps) plus a minor third (3 half-steps). If
the interval between the root and the third of the chord is the major third
(with the minor third between the third and the fifth of the chord), the triad
is amajor chord. If the interval between the root and the third of the chord
is the minor third (and the major third is between the third and fifth of the
chord), then the triad is a minor chord. Listen closely to a major triad and a
minor triad.
Example:
In both major and minor chords,
the fifth of the chord
is a perfect fifth above the root.
e e
In major chords, In minor chords,
the third of the chord the third of the chord
is a major third above the root is a minor third above the root
Example:
Some Major and Minor Triads
C major E major 8? maj. ct maj.
Exercise:
Problem: Write the major chord for each root given.
——
aA _o_ art? 2 ——
7 © ee Re * ‘| pba >——__l 33 —_]
Exercise:
Problem: Write the minor chord for each root given.
Augmented and Diminished Chords
Because they don't contain a perfect fifth, augmented and diminished
chords have an unsettled feeling and are normally used sparingly. An
augmented chord is built from two major thirds, which adds up to an
augmented fifth. A diminished chord is built from two minor thirds, which
add up to a diminished fifth. Listen closely to an augmented triad and a
diminished triad.
Example:
Some Augmented and Diminished Triads
C augmented E aug. B b aug. G aug.
C diminished E dim. B b dim. cH dim.
Exercise:
Problem: Write the augmented triad for each root given.
Exercise:
Problem: Write the diminished triad for each root given.
Solution:
Notice that you can't avoid double sharps or double flats by writing the note
on a different space or line. If you change the spelling of a chord's notes,
you have also changed the chord's name. For example, if, in an
augmented G sharp major chord, you rewrite the D double sharp as an E
natural, the triad becomes an E augmented chord.
G# augmented chord Rewrite D™ as Ef New chord is E augmented
Changing the spelling of any note in a chord
also changes the chord's name.
You can put the chord in a different position or add more of the same-
named notes at other octaves without changing the name of the chord. But
changing the note names or adding different-named notes, will change the
name of the chord. Here is a summary of the intervals in triads in root
position.
Major Chord Minor Chord Augmented Chord Diminished Chord
P5 = perfect fifth
AS = augmented fifth
DS = diminished fifth
M3 = major third
m3 = minor third
Exercise:
Problem:
Now see if you can identify these chords that are not necessarily in
root position. Rewrite them in root position first if that helps.
ee ee ee bi
: —_ai? | Te> | eo | -# ty te
lan» ws | ay | “a> | Da> | | por | ay ee el
| es Tn a ee a oe
_-
Solution:
Chords are rewritten in root position.
Dminor Emajor Caug. A major Bdim. F aug. Dmajor BP minor
Gdim. Adim. Faug. ap minor cRmajor G Rninor D Paug. B bdim.
Beginning Harmonic Analysis
An introduction to chord relationships within a particular key.
Introduction
It sounds like a very technical idea, but basic harmonic analysis just means
understanding how a chord is related to the key and to the other chords in a
piece of music. This can be such useful information that you will find many
musicians who have not studied much music theory, and even some who
don't read music, but who can tell you what the I ("one") or the V ("five")
chord are in a certain key.
Why is it useful to know how chords are related?
e Many standard forms (for example, a "twelve bar blues") follow very
specific chord progressions, which are often discussed in terms of
harmonic relationships.
e If you understand chord relationships, you can transpose any chord
progression you know to any key you like.
e If you are searching for chords to go with a particular melody (in a
particular key), it is very helpful to know what chords are most likely
in that key, and how they might be likely to progress from one to
another.
e Improvisation requires an understanding of the chord progression.
e Harmonic analysis is also necessary for anyone who wants to be able
to compose reasonable chord progressions or to study and understand
the music of the great composers.
Basic Triads in Major Keys
Any chord might show up in any key, but some chords are much more
likely than others. The most likely chords to show up in a key are the
chords that use only the notes in that key (no accidentals). So these chords
have both names and numbers that tell how they fit into the key. (We'll just
discuss basic triads for the moment, not seventh chords or other added-note
or altered chords.) The chords are numbered using Roman numerals from I
to Vii.
Chords in the keys of C major and D major
Cc Dm Em F G Am Bdim
D major
To find all the basic chords in a
key, build a simple triad (in the
key) on each note of the scale.
You'll find that although the
chords change from one key to the
next, the pattern of major and
minor chords is always the same.
Exercise:
Problem:
Write and name the chords in G major and in B flat major. (Hint:
Determine the key signature first. Make certain that each chord begins
on a note in the major scale and contains only notes in the key
signature.) If you need some staff paper, you can print this PDF file
Solution:
G major
BP major [a
a + >:
wl a
You can find all the basic triads that are possible in a key by building one
triad, in the key, on each note of the scale (each scale degree). One easy
way to name all these chords is just to number them: the chord that starts on
the first note of the scale is "I", the chord that starts on the next scale degree
is "ii", and so on. Roman numerals are used to number the chords. Capital
Roman numerals are used for major chords and small Roman numerals for
minor chords. The diminished chord is in small Roman numerals followed
by a small circle. Because major scales always follow the same pattern, the
pattern of major and minor chords is also the same in any major key. The
chords built on the first, fourth, and fifth degrees of the scale are always
major chords (I, IV, and V). The chords built on the second, third, and sixth
on the seventh degree of the scale is a diminished chord.
Note:Notice that IV in the key of B flat is an E flat major chord, not an E
major chord, and vii in the key of G is F sharp diminished, not F
diminished. If you can't name the scale notes in a key, you may find it
difficult to predict whether a chord should be based on a sharp, flat, or
natural note. This is only one reason (out of many) why it is a good idea to
memorize all the scales. (See Major Keys and Scales.) However, if you
don't plan on memorizing all the scales at this time, you'll find it useful to
memorize at least the most important chords (start with I, IV, and V) in
your favorite keys.
A Hierarchy of Chords
Even among the chords that naturally occur in a key signature, some are
much more likely to be used than others. In most music, the most common
chord is I. In Western music, I is the tonal center of the music, the chord
that feels like the "home base" of the music. As the other two major chords
in the key, IV and V are also likely to be very common. In fact, the most
common added-note chord in most types of Western music is a V chord (the
dominant chord) with a minor seventh added (V7). It is so common that this
particular flavor of seventh (a major chord with a minor seventh added) is
often called a dominant seventh, regardless of whether the chord is being
used as the V (the dominant) of the key. Whereas the I chord feels most
strongly "at home", V7 gives the strongest feeling of "time to head home
now". This is very useful for giving music a satisfying ending. Although it
is much less common than the V7, the diminished vii chord (often with a
diminished seventh added), is considered to be a harmonically unstable
chord that strongly wants to resolve to I. Listen to these very short
progressions and see how strongly each suggests that you must be in the
chord (V _- I); G seventh chord to C chord (V7 - I); B diminished seventh
chord to C chord (viidim7 - I) (Please see Cadence for more on this
subject.)
Many folk songs and other simple tunes can be accompanied using only the
I, IV and V (or V7) chords of a key, a fact greatly appreciated by many
beginning guitar players. Look at some chord progressions from real music.
Some chord progressions
A Common Twelve Bar Blues:
7
I
V7 W7 I I
‘7 7 1
Chorus of "Bye Bye, Love"
Iv I Iv I
Iv I W7 OI
Much Western
music is
harmonically
pretty simple,
so it can be
very useful
just to know I,
IV, and V in
your favorite
keys. This
figure shows
progressions
as a list of
chords (read
left to right as
if reading a
paragraph),
one per
measure.
Typically, folk, blues, rock, marches, and Classical-era music is based on
relatively straightforward chord progressions, but of course there are plenty
of exceptions. Jazz and some pop styles tend to include many chords with
added or altered notes. Romantic-era music also tends to use more complex
chords in greater variety, and is very likely to use chords that are not in the
key.
More Complex Chord Progressions
Chorus of "Love Me Tender"
I 17 vi 17
IVM7 w I I
vo VI7 7 17
V7sus4 V7 I I
Beginning of Liszt's "Liebestraum"
I Ill? Vi II7
ii? V7 1 1° J
Bridge of Ellington's "Solitude"
wM7 fIvo I vm7 17
IVM7 fIve I VI7_ iim? V7$s5
Some music has more
complex harmonies.
This can include more
unusual chords such as
major sevenths, and
chords with altered
notes such as sharp
fives. It may also
include more basic
chords that aren't in the
key, such as I
diminished and II
(major), or even chords
based on notes that are
not in the key such as a
sharp IV chord. (Please
see Beyond Triads to
review how to read
chord symbols.)
Extensive study and practice are needed to be able to identify and
understand these more complex progressions. It is not uncommon to find
college-level music theory courses that are largely devoted to harmonic
analysis and its relationship to musical forms. This course will go no further
than to encourage you to develop a basic understanding of what harmonic
analysis is about.
Naming Chords Within a Key
So far we have concentrated on identifying chord relationships by number,
because this system is commonly used by musicians to talk about every
kind of music from classical to jazz to blues. There is another set of names
that is commonly used, particularly in classical music, to talk about
harmonic relationships. Because numbers are used in music to identify
everything from beats to intervals to harmonics to what fingering to use,
this naming system is sometimes less confusing.
Tonic
Supertonic
Mediant
Subdominant
Dominant
Submediant
Subtonic, or Leading Tone
V
vi
vii?
_-
=
iui wueeid
Exercise:
Problem:
Name the chord.
1. Dominant in C major
2. Subdominant in E major
3. Tonic in G sharp major
4. Mediant in F major
9. Supertonic in D major
6. Submediant in C major
7. Dominant seventh in A major
Solution:
1. G major (G)
2. A major (A)
3. G sharp major (G#)
4. A minor (Am)
5. E minor (Em)
6. A minor (Am)
7. E seventh (E7)
Exercise:
Problem:
The following chord progression is in the key of G major. Identify the
relationship of each chord to the key by both name and number. Which
chord is not in the key? Which chord in the key has been left out of the
progression?
G c Am Em
A D Bm D7
G
Solution:
I IV ul vl
G Cc Am Em
tonic subdominant supertonic submediant
i Vv iii V7
D Bm D7
notin key* dominant mediant dominant seventh
I
G
tonic
There is no subtonic in this progression.
*Itis A minor (with a C natural), not A major (with a C sharp)
that belongs in this key. An A major chord can sound good in the key of G major,
however. It is the dominant of the dominant (D major), so playing an
A major chord can sometimes make the music feel like it has temporarily moved
to the (closely related) key of D major. This type of harmonic complexity helps
keep a plece of music interesting.
Minor Keys
Since minor scales follow a different pattern of intervals than major scales,
they will produce chord progressions with important differences from major
key chord progressions.
Exercise:
Problem:
Write (triad) chords that occur in the keys of A minor, E minor, and D
minor. Remember to begin each triad on a note of the natural minor
scale and to include only notes in the scale in each chord. Which chord
relationships are major? Which minor? Which diminished? If you need
staff paper, print this PDF file
Solution:
The tonic, subdominant, and dominant are minor (i, iv, and v). The
mediant, submediant, and subtonic are major (III, VI, and VII). The
supertonic (ii) is diminished.
i n° Il w v VI VU
a minor
e@ minor
d minor
Notice that the actual chords created using the major scale and its relative
minor scale are the same. For example, compare the chords in A minor
({link]) to the chords in C major ([{link]). The difference is in how the
chords are used. As explained above, if the key is C major, the chord
progression will likely make it clear that C is the tonal center of the piece,
for example by featuring the bright-sounding (major) tonic, dominant, and
subdominant chords (C major, G major or G7, and F major), particularly in
strong cadences that end on a C chord.
If the piece is in A minor, on the other hand, it will be more likely to feature
(particularly in cadences) the tonic, dominant, and subdominant of A minor
(the A minor, D minor, and E minor chords). These chords are also
available in the key of C major, of course, but they typically are not given
such a prominent place.
As mentioned above, the "flavor" of sound that is created by a major chord
with a minor seventh added, gives a particularly dominant (wanting-to-go-
to-the-home-chord) sound, which in turn gives a more strong feeling of
tonality to a piece of music. Because of this, many minor pieces change the
dominant chord so that it is a dominant seventh (a major chord with a minor
seventh), even though that requires using a note that is not in the key.
Exercise:
Problem:
Look at the chords in [link]. What note of each scale would have to be
changed in order to make v major? Which other chords would be
affected by this change? What would they become, and are these
altered chords also likely to be used in the minor key?
Solution:
The seventh degree of the scale must be raised by one half step to
make the v chord major. If the seventh scale note is raised, the III
chord becomes augmented, and and the vii chord becomes a
diminished chord (based on the sharp vii rather than the vii). The
augmented III chord would not be particularly useful in the key, but, as
mentioned above, a diminished seventh chord based on the leading
tone (here, the sharp vii) is sometimes used in cadences.
a (harmonic) minor
i i? Wt iw VY VE fii?
The point of the harmonic minor scale is to familiarize the musician with
this common feature of harmony, so that the expected chords become easy
to play in every minor key. There are also changes that can be made to the
melodic lines of a minor-key piece that also make it more strongly tonal.
This involves raising (by one half step) both the sixth and seventh scale
notes, but only when the melody is ascending. So the musician who wants
to become familiar with melodic patterns in every minor key will practice
melodic minor scales, which use different notes for the ascending and
descending scale.
You can begin practicing harmonic analysis by practicing identifying
whether a piece is in the major key or in its relative minor. Pick any piece of
music for which you have the written music, and use the following steps to
determine whether the piece is major or minor:
Is it Major or Minor?
e Identify the chords used in the piece, particularly at the very end, and
at other important cadences (places where the music comes to a
stopping or resting point). This is an important first step that may
require practice before you become good at it. Try to start with simple
music which either includes the names of the chords, or has simple
chords in the accompaniment that will be relatively easy to find and
name. If the chords are not named for you and you need to review how
to name them just by looking at the written notes, see Naming ‘Triads
and Beyond Triads.
e Find the key signature.
e Determine both the major key represented by that key signature, and
its relative minor (the minor key that has the same key signature).
e Look at the very end of the piece. Most pieces will end on the tonic
chord. If the final chord is the tonic of either the major or minor key
for that key signature, you have almost certainly identified the key.
e If the final chord is not the tonic of either the major or the minor key
for that key signature, there are two possibilities. One is that the music
is not in a major or minor key! Music from other cultures, as well as
some jazz, folk, modern, and pre-Baroque European music are based
on other modes or scales. (Please see Modes and Ragas and Scales that
aren’t Major or Minor for more about this.) If the music sounds at all
"exotic" or "unusual", you should suspect that this may be the case.
e If the final chord is not the tonic of either the major or the minor key
for that key signature, but you still suspect that it is in a major or minor
key (for example, perhaps it has a "repeat and fade" ending which
avoids coming to rest on the tonic), you may have to study the rest of
the music in order to discern the key. Look for important cadences
before the end of the music (to identify I). You may be able to identify,
just by listening, when the piece sounds as if it is approaching and
landing on its "resting place". Also look for chords that have that
"dominant seventh" flavor (to identify V). Look for the specific
accidentals that you would expect if the harmonic minor or melodic
minor scales were being used. Check to see whether the major or
minor chords are emphasized overall. Put together the various clues to
reach your final decision, and check it with your music teacher or a
musician friend if possible.
Modulation
Sometimes a piece of music temporarily moves into a new key. This is
called modulation. It is very common in traditional classical music; long
symphony and concerto movements almost always spend at least some time
in a different key (usually a closely related key such as the dominant or
subdominant, or the relative minor or relative major), in order to keep
things interesting. Shorter works, even in classical style, are less likely to
have complete modulations. Abrupt changes of key can seem unpleasant
and jarring. In most styles of music, modulation is accomplished gradually,
using a progression of chords that seems to move naturally towards the new
key. But implied modulations, in which the tonal center seems to suddenly
shift for a short time, can be very common in some shorter works (jazz
standards, for example). As in longer works, modulation, with its new set of
chords, is a good way to keep a piece interesting. If you find that the chord
progression in a piece of music suddenly contains many chords that you
would not expect in that key, it may be that the piece has modulated. Lots of
accidentals, or even an actual change of key_signature, are other clues that
the music has modulated.
A new key signature may help you to identify the modulation key. If there
is not a change of key signature, remember that the new key is likely to
contain whatever accidentals are showing up. It is also likely that many of
the chords in the progression will be chords that are common in the new
key. Look particularly for tonic chords and dominant sevenths. The new key
is likely to be closely related to the original key, but another favorite trick in
popular music is to simply move the key up one whole step, for example
from C major to D major. Modulations can make harmonic analysis much
more challenging, so try to become comfortable analyzing easier pieces
before tackling pieces with modulations.
Further Study
Although the concept of harmonic analysis is pretty basic, actually
analyzing complex pieces can be a major challenge. This is one of the main
fields of study for those who are interested in studying music theory at a
more advanced level. One next step for those interested in the subject is to
become familiar with all the ways notes may be added to basic triads.
(Please see Beyond Triads for an introduction to that subject.) At that point,
you may want to spend some time practicing analyzing some simple,
familiar pieces. Depending on your interests, you may also want to spend
time creating pleasing chord progressions by choosing chords from the
correct key that will complement a melody that you know. As of this
writing, the site Music Theory for Songwriters featured "chord maps" that
help the student predict likely chord progressions.
For more advanced practice, look for music theory books that focus entirely
on harmony or that spend plenty of time analyzing harmonies in real music.
(Some music history textbooks are in this category.) You will progress more
quickly if you can find books that focus on the music genre that you are
most interested in (there are books specifically about jazz harmony, for
example).
Cadence in Music
A cadence is a place in a piece of music that feels like a stopping or resting
point. In tonal music, cadences are classified by their chord progressions.
A cadence is any place in a piece of music that has the feel of an ending
point. This can be either a strong, definite stopping point - the end of the
piece, for example, or the end of a movement or a verse - but it also refers
to the "temporary-resting-place" pauses that round off the ends of musical
ideas within each larger section.
A musical phrase, like a sentence, usually contains an understandable idea,
and then pauses before the next idea starts. Some of these musical pauses
are simply take-a-breath-type pauses, and don't really give an "ending"
feeling. In fact, like questions that need answers, many phrases leave the
listener with a strong expectation of hearing the next, "answering", phrase.
Other phrases, though, end with a more definite "we've arrived where we
were going” feeling. The composer's expert control over such feelings of
expectation and arrival are one of the main sources of the listener's
enjoyment of the music.
Like a story, a piece of music can come to an end by simply stopping, but
most listeners will react to such abruptness with dissatisfaction: the story or
music simply "stopped" instead of "ending" properly. A more satisfying
ending, in both stories and music, is usually provided by giving clues that
an end is coming, and then ending in a commonly-accepted way. Stories are
also divided into paragraphs, chapters, stanzas, scenes, or episodes, each
with their own endings, to help us keep track of things and understand what
is going on. Music also groups phrases and motifs into verses, choruses,
sections, and movements, marked off by strong cadences to help us keep
track of them. In good stories, there are clues in the plot and the pacing - in
the Western tradition, the chase gets more exciting, characters good and bad
get what they deserve, the inevitable tragedy occurs, or misunderstandings
get resolved - that signal that the end of the story is nearing. Similarly, in
music there are clues that signal to the listener that the end is coming up.
These clues may be in the form; in the development of the musical ideas; in
the music's tempo, texture, or rhythmic complexity; in the chord
progression; even in the number and length of the phrases (Western
listeners are fond of powers of two). Like the ending of a story, an ending in
music is more satisfying if it follows certain customs that the listener
expects to hear. If you have grown up listening to a particular musical
tradition, you will automatically have these expectations for a piece of
music, even if you are not aware of having them. And like the customs for
storytelling, these expectations can be different in different musical
traditions.
Some things that produce a feeling of cadence
e Harmony - In most Western and Western-influenced music (including
jazz and "world" musics), harmony is by far the most important signal
of cadence. One of the most fundamental "rules" of the major-minor
harmony system is that music ends on the tonic. A tonal piece of music
will almost certainly end on the tonic chord, although individual
phrases or sections may end on a different chord (the dominant is a
popular choice). But a composer cannot just throw in a tonic chord and
expect it to sound like an ending; the harmony must "lead up to" the
ending and make it feel inevitable (just as a good story makes the
ending feel inevitable, even if it's a surprise). So the term cadence, in
tonal music, usually refers to the "ending" chord plus the short chord
progression that led up to it. There are many different terms in use for
the most common tonal cadences; you will find the most common
terms below. Some (but not all) modal musics also use harmony to
indicate cadence, but the cadences used can be quite different from
those in tonal harmony.
¢ Melody - In the major/minor tradition, the melody will normally end
on some note of the tonic chord triad, and a melody ending on the
tonic will give a stronger (more final-sounding) cadence than one
ending on the third or fifth of the chord. In some modal musics, the
melody plays the most important role in the cadence. Like a scale,
each mode also has a home note, where the melody is expected to end.
A mode often also has a formula that the melody usually uses to arrive
at the ending note. For example, it may be typical of one mode to go to
the final note from the note one whole tone below it; whereas in
another mode the penultimate note may be a minor third above the
final note. (Or a mode may have more than one possible melodic
cadence, or its typical cadence may be more complex.)
e¢ Rhythm - Changes in the rhythm, a break or pause in the rhythm, a
change in the tempo, or a slowing of or pause in the harmonic rhythm
are also commonly found at a cadence.
e Texture - Changes in the texture of the music also often accompany a
cadence. For example, the music may momentarily switch from
harmony to unison or from counterpoint to a simpler block-chord
homophony.
e Form - Since cadences mark off phrases and sections, form and
cadence are very closely connected, and the overall architecture of a
piece of music will often indicate where the next cadence is going to
be - every eight measures for a certain type of dance, for example.
(When you listen to a piece of music, you actually expect and listen for
these regularly-spaced cadences, at least subconsciously. An
accomplished composer may "tease" you by seeming to lead to a
cadence in the expected place, but then doing something unexpected
instead.)
Harmonic analysis, form, and cadence in Western music are closely
interwoven into a complex subject that can take up an entire course at the
college-music-major level. Complicating matters is the fact that there are
several competing systems for naming cadences. This introductory course
cannot go very deeply into this subject, and so will only touch on the
common terms used when referring to cadences. Unfortunately, the various
naming systems may use the same terms to mean different things, so even a
list of basic terms is a bit confusing.
Some Tonal Cadence Terms
e Authentic - A dominant chord followed by a tonic chord (V-I, or often
V7-I).
e Complete Cadence - same as authentic cadence.
¢ Deceptive Cadence - This refers to times that the music seems to lead
up to a cadence, but then doesn't actually land on the expected tonic,
and also often does not bring the expected pause in the music. A
deceptive cadence is typically in a major key, and is the dominant
followed by the submediant (V-vi). This means the substituted chord is
the relative minor of the tonic chord.
e False Cadence - Same as deceptive cadence.
Full Close - Same as authentic cadence.
Half-cadence - May refer to a cadence that ends on the dominant
chord (V). This type of cadence is more common at pause-type
cadences than at full-stop ones. OR may have same meaning as plagal
cadence.
Half close - Same as plagal cadence.
Imperfect Cadence - May refer to an authentic (V-I) cadence in which
the chord is not in root position, or the melody does not end on the
tonic. OR may mean a cadence that ends on the dominant chord (same
as one meaning of half-cadence).
Interrupted Cadence - Same as deceptive cadence.
Perfect Cadence - Same as authentic cadence. As its name suggests,
this is considered the strongest, most final-sounding cadence. Some do
not consider a cadence to be completely perfect unless the melody
ends on the tonic and both chords (V and I) are in root position.
Plagal Cadence - A subdominant chord followed by a tonic chord (IV-
I). For many people, this cadence will be familiar as the "Amen"
chords at the end of many traditional hymns.
Semi-cadence - Same possible meanings as half cadence.
You can listen to a few simple cadences here: Perfect Cadence, Plagal
Cadence, Half-cadence, Deceptive Cadence. The figure below also shows
some very simple forms of some common cadences. The first step in
becoming comfortable with cadences is to start identifying them in music
that is very familiar to you. Find the pauses and stops in the music. Do a
harmonic analysis of the last few chords before each stop, and identify what
type of cadence it is. Then see if you can begin to recognize the type of
cadence just by listening to the music.
Examples of Common Cadences
Vv |
S———=—
e)
_ 2
o
Perfect Cadence in C
major
—————
Plagal Cadence in C
major
Deceptive Cadence in
C major
Exercise:
Problem:
Identify the type of cadence in each excerpt. (Hint: First identify the
key and then do a harmonic analysis of the progression.
Solution:
(Perfect) Authentic Plagal
inEflat major: I Vv I inGmajo: ow IV I
Half-cadence (Perfect) Authentic
in F major: IM7 U7 Vv inDminor: 1 i? i V i
inC major; IVM7 W7 I
(temporary modulation to V)
Notice that the half cadence looks like (and in fact is) a modulation to
the dominant. In this very common progression, the dominant seventh
of the dominant (which requires an accidental) makes the dominant
feel like a very strong resting point, and the piece will continue on in
the dominant key for a while, before returning to the tonic key. Also
notice the accidental required in the minor key to make the (major)
dominant chord.
Consonance and Dissonance
Consonance and dissonance are musical terms describing whether
combinations of notes sound good together or not.
Notes that sound good together when played at the same time are called
consonant. Chords built only of consonances sound pleasant and "stable";
you can listen to one for a long time without feeling that the music needs to
change to a different chord. Notes that are dissonant can sound harsh or
unpleasant when played at the same time. Or they may simply feel
"unstable"; if you hear a chord with a dissonance in it, you may feel that the
music is pulling you towards the chord that resolves the dissonance.
Obviously, what seems pleasant or unpleasant is partly a matter of opinion.
This discussion only covers consonance and dissonance in Western music.
Note: For activities that introduce these concepts to young students, please
see Consonance and Dissonance Activities.
Of course, if there are problems with tuning, the notes will not sound good
together, but this is not what consonance and dissonance are about. (Please
note, though, that the choice of tuning system can greatly affect which
intervals sound consonant and which sound dissonant! Please see ‘Tuning
Systems for more about this.)
Consonance and dissonance refer to intervals and chords. The interval
between two notes is the number of half steps between them, and all
intervals have a name that musicians commonly use, like major third
(which is 4 half steps), perfect fifth (7 half steps), or octave. (See Interval to
learn how to determine and name the interval between any two notes.)
An interval is measured between two notes. When there are more than two
notes sounding at the same time, that's a chord. (See Triads, Naming
Triads, and Beyond Triads for some basics on chords.) Of course, you can
still talk about the interval between any two of the notes in a chord.
The simple intervals that are considered to be consonant are the minor third,
major third, perfect fourth, [missing_resource: fifth.mid]minor sixth, major
sixth, and the [missing_resource: octave.mid]
Consonant Intervals
e oO oa o ao oa
Minor Major Perfect Perfect Minor Major Octave
Third Third Fourth Fifth Sixth Sixth
In modern Western Music, all of these intervals are considered to be
pleasing to the ear. Chords that contain only these intervals are considered
to be "stable", restful chords that don't need to be resolved. When we hear
them, we don't feel a need for them to go to other chords.
The intervals that are considered to be dissonant are the minor second, the
major second, the minor seventh, the major seventh, and particularly the
tritone, which is the interval in between the perfect fourth and perfect fifth.
Dissonant Intervals
e oO oOo oOo
Minor Major Tritone Minor Major
Second Second Seventh Seventh
These intervals are all considered to be somewhat unpleasant or tension-
producing. In tonal music, chords containing dissonances are considered
"unstable"; when we hear them, we expect them to move on to a more
stable chord. Moving from a dissonance to the consonance that is expected
to follow it is called resolution, or resolving the dissonance. The pattern of
tension and release created by resolved dissonances is part of what makes a
piece of music exciting and interesting. Music that contains no dissonances
can tend to seem simplistic or boring. On the other hand, music that
contains a lot of dissonances that are never resolved (for example, much of
twentieth-century "classical" or "art" music) can be difficult for some
people to listen to, because of the unreleased tension.
Resolving Dissonances
Dsus4 D
Maj. 2nd Min. 7th
Clusters of Seconds (unresolved)
Min. 2nd
In most music a dissonance will
resolve; it will be followed by a
consonant chord that it naturally leads
to, for example a G seventh chord
resolves to a C major chord, and a D
suspended fourth resolves to a D
major chord. A series of unresolved
dissonances, on the other hand, can
produce a sense of unresolved
tension.
Why are some note combinations consonant and some dissonant?
Preferences for certain sounds is partly cultural; that's one of the reasons
why the traditional musics of various cultures can sound so different from
each other. Even within the tradition of Western music, opinions about what
is unpleasantly dissonant have changed a great deal over the centuries. But
consonance and dissonance do also have a strong physical basis in nature.
In simplest terms, the sound waves of consonant notes "fit" together much
better than the sound waves of dissonant notes. For example, if two notes
are an octave apart, there will be exactly two waves of one note for every
one wave of the other note. If there are two and a tenth waves or eleven
twelfths of a wave of one note for every wave of another note, they don't fit
together as well. For much more about the physical basis of consonance and
dissonance, see Acoustics for Music Theory, Harmonic Series, and ‘Tuning
systems.
Beyond Triads: Naming Other Chords
The name of a chord is determined by the relationship to the tonic of every
note in the chord.
Introduction
Once you know how to name triads (please see Triads and Naming Triads),
you need only a few more rules to be able to name all of the most common
chords.
This skill is necessary for those studying music theory. It's also very useful
at a "practical" level for composers, arrangers, and performers (especially
people playing chords, like pianists and guitarists), who need to be able to
talk to each other about the chords that they are reading, writing, and
playing.
Chord manuals, fingering charts, chord diagrams, and notes written out on a
staff are all very useful, especially if the composer wants a very particular
sound on a chord. But all you really need to know are the name of the
chord, your major scales and minor scales, and a few rules, and you can
figure out the notes in any chord for yourself.
What do you need to know to be able to name most chords?
1. You must know your major, minor, augmented and diminished triads.
Either have them all memorized, or be able to figure them out
following the rules for triads. (See Triads and Naming Triads.)
2. You must be able to find intervals from the root of the chord. One way
to do this is by using the rules for intervals. (See Interval.) Or if you
know your scales and don't want to learn about intervals, you can use
the method in #3 instead.
3. If you know all your scales (always a good thing to know, for so many
reasons), you can find all the intervals from the root using scales. For
example, the "4" in Csus4 is the 4th note in a C (major or minor) scale,
and the "minor 7th" in Dm7 is the 7th note in a D (natural) minor
scale. If you would prefer this method, but need to brush up on your
scales, please see Major Keys and Scales and Minor Keys and Scales.
4. You need to know the rules for the common seventh chords, for
extending and altering chords, for adding notes, and for naming bass
notes. The basic rules for these are all found below.
Note:Please note that the modern system of chord symbols, discussed
below, is very different from the figured bass shorthand popular in the
seventeenth century (which is not discussed here). For example, the "6" in
figured bass notation implies the first inversion chord, not an added 6. (As
of this writing, there was a very straightforward summary of figured bass
at Ars Nova Software.)
Chord Symbols
Some instrumentalists, such as guitarists and pianists, are sometimes
expected to be able to play a named chord, or an accompaniment based on
that chord, without seeing the notes written out in common notation. In
such cases, a chord symbol above the staff tells the performer what chord
should be used as accompaniment to the music until the next symbol
appears.
Chord Symbols
He'd ne'er leave the girl with the straw-ber-ry curls and the band played on.
A chord symbol above the staff is sometimes the only
indication of which notes should be used in the
accompaniment. Chord symbols also may be used even
when an accompaniment is written out, so that
performers can read either the chord symbol or the
notated music, as they prefer.
There is widespread agreement on how to name chords, but there are
several different systems for writing chord symbols. Unfortunately, this can
be a little confusing, particularly when different systems use the same
symbol to refer to different chords. If you're not certain what chord is
wanted, you can get useful clues both from the notes in the music and from
the other chord symbols used. (For example, if the "minus" chord symbol is
used, check to see if you can spot any chords that are clearly labelled as
either minor or diminished.)
Examples of Chord Symbol Variety
Major chord Cc CMaj €
Minor chord cm Cmin ¢-
Augmented Chord Caug Ct
Diminished Chord* Cdim C—
Major Seventh CM7- = CMaj7 co coy Cc?
Minor Seventh Cm7 Cmin7 G-F
Diminished Seventh* Cdim7 C°?
*It is so common to add the (diminished) seventh to the
diminished chord, that the symbol for the
diminished chord may be used with the assumption that
you will add the diminished seventh.
There is unfortunately a wide
variation in the use of chord
symbols. In particular, notice that
some symbols, such as the
"minus" sign and the triangle, can
refer to different chords,
depending on the assumptions of
the person who wrote the symbol.
Seventh Chords
If you take a basic triad and add a note that is a seventh above the root, you
have a seventh chord. There are several different types of seventh chords,
distinguished by both the type of triad and the type of seventh used. Here
are the most common.
Seventh Chords
e Seventh (or "dominant seventh") chord = major triad + minor seventh
e Major Seventh chord = major triad + major seventh
e Minor Seventh chord = minor triad + minor seventh
e Diminished Seventh chord = diminished triad + diminished seventh
(half step lower than a minor seventh)
e Half-diminished Seventh chord = diminished triad + minor seventh
An easy way to remember where each seventh is:
e The major seventh is one half step below the octave.
e The minor seventh is one half step below the major seventh.
¢ The diminished seventh is one half step below the minor seventh.
Common Seventh Chords
C7 CMaj7_—s Cmin7 ce? ¢*
dominant major minor diminished half-diminished
seventh seventh seventh seventh seventh
Listen to the differences between the C seventh, C major seventh, C minor
seventh, C diminished seventh, and C half-diminished seventh.
Exercise:
Problem:
Write the following seventh chords. If you need staff paper, you can
print this PDF file
1. G minor seventh
2. E (dominant) seventh
3. B flat major seventh
4. D diminished seventh
5. F (dominant) seventh
6. F sharp minor seventh
7. G major seventh
8. B half-diminished seventh
Solution:
Gm7 E7 BDMaj7 Ddim7 __—F7 Femz7 GMaj7_—s B®
ve 6 a eS a
rE rs es ee
Exercise:
Problem:
Write a Ddim7, Fdim7, G#dim7, and Bdim7. Look closely at the
chords you have written and see if you can notice something surprising
about them. (Hint: try rewriting the chords enharmonically so that all
the notes are either natural or (single) flat.
Solution:
Respell each chord so that you are only using
natural and (single) flat notes:
All of the chords contain the (enharmonic) equivalent
of the same four notes:D,F, A?,andB,
so these chords sound like inversions of each other.
There are two other sets of enharmonically
equivalent diminished seventh chords;
how quickly can you find them?
Added Notes, Suspensions, and Extensions
The seventh is not the only note you can add to a basic triad to get a new
chord. You can continue to extend the chord by adding to the stack of
thirds, or you can add any note you want. The most common additions and
extensions add notes that are in the scale named by the chord.
Extending and Adding Notes to Chords
C major C(add 9) chord
e ; e :
12 3 4 5 6 7 8 9 10 11 #%12 #13 ~~ «*e@te.
D major D6 chord
1 3 4 5 6 7 8 9 10 11 12 #13 ete.
apart 1) chord
F minor
6 7 8 9 10 11
To find out what to call a note added to a chord, count
the notes of the scale named by the chord.
The first, third, and fifth (1, 3, and 5) notes of the scale are part of the basic
triad. So are any other notes in other octaves that have the same name as 1,
3, or 5. Ina C major chord, for example, that would be any C naturals, E
naturals, and G naturals. If you want to add a note with a different name,
just list its number (its scale degree) after the name of the chord.
Adding to and Extending Chords
c Csus4 C6 Csus9 c9 Cadd13 C13 c13
Labelling a number as "sus" (suspended) implies
that it replaces the chord tone immediately below
it. Labelling it "add" implies that only that note is
added. In many other situations, the performer is
left to decide how to play the chord most
effectively. Chord tones may or may not be left
out. In an extended chord, all or some of the notes
in the "stack of thirds" below the named note may
also be added.
Many of the higher added notes are considered extensions of the "stack of
thirds" begun in the triad. In other words, a C13 can include (it's sometimes
the performer's decision which notes will actually be played) the seventh,
ninth, and eleventh as well as the thirteenth. Such a chord can be dominant,
major, or minor; the performer must take care to play the correct third and
seventh. If a chord symbol says to "add13", on the other hand, this usually
means that only the thirteenth is added.
A Variety of Ninth Chords
c9 cM9 Cm9 Cadd9
Take care to use the correct
third and seventh - dominant,
major, or minor - with
extended chords. If the higher
note is labelled "add", don't
include the chord extensions
that aren't named.
Note:All added notes and extensions, including sevenths, introduce
dissonance into the chord. In some modern music, many of these
dissonances are heard as pleasant or interesting or jazzy and don't need to
be resolved. However, in other styles of music, dissonances need to be
resolved, and some chords may be altered to make the dissonance sound
less harsh (for example, by leaving out the 3 in a chord with a 4).
You may have noticed that, once you pass the octave (8), you are repeating
the scale. In other words, C2 and C9 both add a D, and C4 and C11 both
add an F, It may seem that C4 and C11 should therefore be the same chords,
but in practice these chords usually do sound different; for example,
performers given a C4 chord will put the added note near the bass note and
often use it as a temporary replacement for the third (the "3") of the chord.
On the other hand, they will put the added note of a C11 at the top of the
chord, far away from the bass note and piled up on top of all the other notes
of the chord (including the third), which may include the 7 and 9 as well as
the 11. The result is that the C11 - an extension - has a more diffuse, jazzy,
or impressionistic sound. The C4, on the other hand, has a more intense,
needs-to-be-resolved, classic suspension sound. In fact, 2, 4, and 9 chords
are often labelled suspended (sus), and follow the same rules for resolution
in popular music as they do in classical.
Csus4 C cll
e e Oo
Low-number added notes and
high-number added notes are
treated differently. So even though
they both add an F, a C4
suspension will sound quite
different from a C11 extended
chord.
Bass Notes
The bass line of a piece of music is very important, and the
composer/arranger often will want to specify what note should be the
lowest-sounding in the chord. At the end of the chord name will be a slash
followed by a note name, for example C/E. The note following the slash
should be the bass note.
Naming the Bass Note
C/G c/B
re
The note
following
the slash is
the bass
note of the
chord. It
can bea
note that is
already in
the chord -
making the
chord a
first or
second
inversion -
or it can be
an added
note,
following
the same
basic rules
as other
added notes
(including
using it to
replace
other notes
in the
chord).
The note named as the bass note can be a note normally found in the chord -
for example, C/E or C/G - or it can be an added note - for example C/B or
C/A. If the bass note is not named, it is best to use the tonic as the primary
bass note.
Exercise:
Problem:
Name the chords. (Hint: Look for suspensions, added notes,
extensions, and basses that are not the root. Try to identify the main
triad or root first.)
Solution:
Em(add 11) F13 G9 Asus4 F/C Am/G F6
Exercise:
Problem:
For guitarists, pianists, and other chord players: Get some practical
practice. Name some chords you don't have memorized (maybe F6,
Am/G, Fsus4, BM7, etc.). Chords with fingerings that you don't know
but with a sound that you would recognize work best for this exercise.
Decide what notes must be in those chords, find a practical fingering
for them, play the notes and see what they sound like.
Solution:
You can check your work by
¢ listening to the chords to see if they sound correct
e playing your chords for your teacher or other trained musician
e checking your answers using a chord manual or chord diagrams
Altering Notes and Chords
If a note in the chord is not in the major or minor scale of the root of the
chord, it is an altered note and makes the chord an altered chord. The
alteration - for example "flat five" or "sharp nine" - is listed in the chord
symbol. Any number of alterations can be listed, making some chord
symbols quite long. Alterations are not the same as accidentals.
Remember, a chord symbol always names notes in the scale of the chord
root, ignoring the key signature of the piece that the chord is in, so the
alterations are from the scale of the chord, not from the key of the piece.
Altered Chords
Two possible ¢7#sb9 pb13 Hi
chord symbols
for each chord:
o7*3 pbi3+11
e by
C dominant seventh B flat thirteenth chord
with a sharp 5 with a sharp eleven
and flat nine
There is some variation in the chord
symbols for altered chords. Plus/minus
or sharp/flat symbols may appear before
or after the note number. When sharps
and flats are used, remember that the
alteration is always from the scale of the
chord root, not from the key signature.
Exercise:
Problem:
On a treble clef staff, write the chords named. You can print this PDF
file if you need staff paper for this exercise.
1. D (dominant) seventh with a flat nine
2. A minor seventh with a flat five
3. G minor with a sharp seven
4. B flat (dominant) seventh with a sharp nine
5. F nine sharp eleven
Solution:
Notice that a half-diminished seventh can be (and sometimes is)
written as it is here, as a minor seventh with flat five.
p7~9 Am7~5 Gm
Note that a “half-diminished seventh" may be written as a
“minor seventh with flat five", as it is here.
The “minor chord with sharp seventh" is sometimes referred to
as a "minor, major seventh" chord,forexample Gm?
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